I know how you feel, because it's that way of thinking that was the catalyst to starting the group I'm the president of! I feel for the PTAers who don't subscribe to this type of behavior as well, because it's morons like this that ruin it for everyone, whether they be a PTA, PTO, HPA... WHATEVER. This sort of nonsence is like the flu--it doen't single our just one particular group; it can happen anywhere.
Starting your own group isn't too hard, and with the principal's blessing (how's your BOE?) it makes it much easier. We have marginal support from our principal, but our BOE and Superintendent have been supportive, which has been our one saving grace.
If you're going on your own--be prepared, it's not cheap to get "official," nor is it for the faint of heart when it comes putting up with resistance, which it sounds like you're SURE to get from this lot. I don't know how territorial they are, but if they gave you a hard time as president, be sure to expect problems with a new group. With support you can get past it, but it can be extraordinarily taxing and aggravating. If the PTA is as strong as you say it is in your area, be prepared from nonsence on higher levels as well. Not to pee on your parade, but speaking from experience I'd hate to see you go through an ordeal if you didn't have to.
Our group got it's start more because of finances, and PTA board attitudes that aren't sanctioned by the "PTA," but its organization did lend itself to supporting the crap we were subject to (the catalyst for us was a playground we were told the PTA could not be supportive of). We would be voted down on a lot of things because we were told it was too expensive, and the fundraising needed was not what the "PTA" is about. So we started our own group (not a PTO) to raise funds for the playground, and once that's done, we plan on moving ahead to fund a host of things our school could use--a newspaper, drama club, more family involvement/fun programs. We are still involved with our PTA, and support the programs they have in place, and in fact hope to support the PTA with our finances in the future. We've had to be more flexible and swallow a lot of pride to get where we are, but little by little we're gaining ground. One problem for us that prevented us from taking over the PTA board (and thus saving us the aggravation of starting our own group) was that our school has no underlying parent support system; people would agree with what we were saying, but when it came to taking on the board, forget it. No one wanted to, even though there were more of us than them. Having ur own group has allowed us freedom of action in many ways with small numbers for support.
Since you were president and had some power to influence people, I'd personally take back the presidency and move from there. Especially if you have support. Either way you'd get grief, at least that way you'd save yourself the time, effort, money etc. of setting up a new group. If you do decide to go the route of starting your own group though, feel free to email me, I'll help with whatever I can!